High performance equalizer having reduced complexity

ABSTRACT

An apparatus and method for implementing an equalizer which combines the benefits of a decision feedback equalizer (DFE) with a maximum-a-posterori (MAP) equalizer (or a maximum likelihood sequence estimator, MLSE) to provide an equalization device with significantly lower complexity than a full-state MAP device, but which still provides improved performance over a conventional DFE. The equalizer architecture includes two DFE-like structures, followed by a MAP equalizer. The first DFE forms tentative symbol decisions. The second DFE is used thereafter to truncate the channel response to a desired memory of L 1  symbols, which is less than the total delay spread of L symbols of the channel. The MAP equalizer operates over a channel with memory of L 1  symbols (where L 1 &lt;=L), and therefore the overall complexity of the equalizer is significantly reduced.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of U.S. patent applicationSer. No. 11/376,002, filed Mar. 14, 2006, now U.S. Pat. No. 7,656,943,which is a continuation of U.S. patent application Ser. No. 09/941,300,filed Aug. 27, 2001, now U.S. Pat. No. 7,012,957, which claims priorityof the following—U.S. Provisional patent application having Ser. No.60/265,740, entitled “A Decision Feedback Equalizer for Minimum andMaximum Phase Channels,” filed Feb. 1, 2001; U.S. Provisional patentapplication having Ser. No. 60/265,736 entitled “Method For ChannelEqualization For TDMA Cellular Communication Systems,” filed Feb. 1,2001; and U.S. Provisional patent application having Ser. No.60/279,907, entitled “A Novel Approach to the Equalization of EDGESignals,” filed Mar. 29, 2001; all of which are hereby incorporated byreference in their entirety.

The application is also related to U.S. patent application having Ser.No. 09/941,027, entitled “Decision Feedback Equalizer for Minimum andMaximum Phase Channels,” filed Aug. 27, 2001, now U.S. Pat. No.7,006,563, and hereby incorporated by reference.

FIELD OF THE INVENTION

The present invention provides an improved method and apparatus forchannel equalization in communication systems, wherein the advantages ofa decision feedback equalizer (DFE) are combined with those of anon-linear equalizer, including a maximum-a-posteriori (MAP) ormaximum-likelihood sequence estimator (MLSE) equalizer.

BACKGROUND OF THE INVENTION

This invention addresses the receiver design for digital communicationsystems employing high-order modulation schemes and operating in highlytemporally dispersive channels. As an example, this invention has beenapplied to the EDGE standard (“Digital Cellular Communication System(Phase 2+) (GSM 05.01-GSM 05.05 version 8.4.0 Release 1999)”). The EDGEstandard is built on the existing GSM standard, using the sametime-division multiple access (TDMA) frame structure. EDGE uses 8-PSK(Phase-shift keying) modulation, which is a high-order modulation thatprovides for high-data-rate services. In 8-PSK modulation, threeinformation bits are conveyed per symbol by modulating the carrier byone of eight possible phases.

A wireless channel is often temporally dispersive. In other words, aftera signal is transmitted, a system will receive multiple copies of thatsignal with different channel gains at various points in time. This timedispersion in the channel causes inter-symbol interference (ISI) whichdegrades the performance of the system. FIG. 1 shows a prior art exampleof a multipath channel profile. The main signal cursor 102 is followedin time by post-cursors 104, 106, 108, and 110.

To combat the effects of ISI at the receiver, many different types ofequalization techniques can be used. One popular equalization techniqueuses a Decision Feedback Equalizer (DFE). The DFE cancels the extraneousmultipath components to eliminate the deleterious effects of ISI. A DFEis relatively simple to implement and performs well under certain knowncircumstances. The performance of the DFE depends heavily on thecharacteristics of the channel. A DFE typically performs well over aminimum-phase channel, where the channel response has little energy inits pre-cursors, and its post-cursor energy decays with time. A DFEtypically consists of a feed-forward filter (FFF) and a feedback filter(FBF). The FFF is used to help transform the channel into such aminimum-phase channel. Methods for computing the coefficients of the FFFand FBF (based upon channel estimates) are well known. See, e.g., N.Al-Dhahir and J. M. Cioffi, “Fast Computation of Channel-Estimate BasedEqualizers in Packet Data Transmission,” IEEE Trans. Signal Processing,vol. 43, pp. 2462-2473, November 1995, the contents of which areincorporated herein by reference.

Certain advantages of a DFE include good performance with relatively lowcomplexity. Certain disadvantages include, but are not limited to: (1)Error propagation—i.e., once an error is made, that error is fed backand propagated into future symbol decisions. (2) Sub-optimumperformance—i.e., instead of capturing multipath energy in the channel,the DFE instead cancels out this energy. (3) Hard decision output—i.e.,a DFE makes a decision on the transmitted symbol without providing anyinformation associated with the reliability of that decision.

Other more complex equalization techniques utilize the multipath energyfrom the received signal, rather than trying to cancel the energy. Suchequalizers include, but are not limited to, MLSE (Maximum LikelihoodSequence Estimation) and MAP (Maximum A Posteriori) Estimation. Thesenon-linear equalization techniques make a determination as to the mostlikely transmitted symbols, based upon all of the available informationto the receiver. The MLSE is the optimum sequence estimator over afinite channel response. The complexity of the MLSE equalizer growsexponentially with the channel response duration, and the equalizerproduces hard symbol decisions. The MAP equalizer operates in a similarfashion to the MLSE equalizer but provides soft symbol decisions. Theprimary disadvantage of the MAP equalizer is complexity. Hence, whilethese example equalizers are better at handling problematic signals,their implementations can prove to be very complex and expensive forsystems using high-order modulation, such as the EDGE system. See G.David Forney. Jr., “Maximum-Likelihood Sequence Estimation of DigitalSequences in the Presence of Intersymbol Interference,” IEEE Trans.Inform. Theory, vol. 18, pp. 363-377, May 1972; J. G. Proakis, “DigitalCommunications,” (3^(rd) edition) New York; McGraw-Hill, 1995. Thecontents of both the foregoing references are incorporated herein byreference.

The complexity of the MLSE and MAP equalizers, implemented using theknown Viterbi algorithm (or the like), is exponentially proportional tothe memory of the channel. In particular, the number of states requiredin the MLSE or MAP equalizer is given by M^(L), where M is the size ofthe symbol alphabet and L is the memory of the channel in symbols.Moreover, the use of 8PSK modulation in the EDGE system makes thecomplexity of the MLSE and MAP equalizers very large for channels withmoderate delay spreads. Note that different channel models exist fordifferent types of terrain and are used to quantify receiver sensitivityin the GSM standard. For example, the Hilly Terrain (HT) channel modelhas a profile that spans more than five symbols and would thereforerequire an MLSE or MAP equalizer with 32,768 states to achieveacceptable performance.

Techniques to reduce the number of states of the MLSE have beenproposed. See, e.g., Alexandra Duel-Hallen and Chris Heegard, “Delayeddecision-feedback sequence estimation,” IEEE Transactions onCommunications, vol. 37, no. 5, p. 428-436, May 1989; M. Vedat Eybogluand Shahid U. Qureshi, “Reduced-state sequence estimation with setpartitioning and decision feedback,” IEEE Transactions onCommunications, vol. 36, no. 1, pp. 13-20, January 1988. Under thesetechniques, a subset of the full state space is chosen as the statespace, and a DFE is implemented on every state of the trellis (i.e., asshown in a state space diagram). However, the complexity of computingthe path metric values in these algorithms is still very large forchannels with a large delay spread.

Accordingly, what is needed in the field of the art is an equalizerdevice that provides for a simpler implementation, such as a DFE, butwhich provides the improved performance characteristics of a morecomplex equalizer, such as an MLSE or MAP. The equalizer should begenerally applicable to all digital communication systems but provideparticular advantage to coded systems using higher-order modulationschemes.

SUMMARY OF THE INVENTION

The present invention describes an equalizer which combines the benefitsof a decision feedback equalizer (DFE) with a maximum-a-posterori (MAP)equalizer (or a maximum likelihood sequence estimator, MLSE) to providean equalization device with lower complexity than a full-state MAP orMLSE device, but which still provides improved performance over a pureDFE solution.

In the present invention, the equalizer architecture includes twoDFE-like structures, followed by a MAP equalizer. The channel responseis estimated and used to derive the coefficients of the feed-forward andfeedback filters. The coefficients of the feedback filter of the secondDFE are a subset of the coefficients of the first feedback filter.

The first DFE acts like a conventional DFE and forms tentative symboldecisions. The second DFE is used thereafter to eliminate, or subtract,the impact of certain post-cursors that exist past a certain memory, L₁,(where L₁<=L) of the channel, by using the tentative decisions formed bythe first DFE. The effective channel response seen by the MAP equalizeris therefore constrained to a memory L₁, and therefore the overallcomplexity of the equalizer is significantly reduced. When the value ofL₁ is zero, the proposed equalizer degenerates to a conventional DFE.When the value of L₁=L, the proposed equalizer is a full state MAPequalizer. Therefore performance versus complexity trade-offs between asimple DFE and a full-state MAP equalizer can be made.

An MLSE equalizer might also be used in place of the MAP equalizer inthe described configuration, if further complexity reduction is desired.However, usage of the MLSE will come at the expense of receiversensitivity.

Accordingly, one aspect of the present invention provides for areduced-state complexity equalizer apparatus for use with communicationsystems requiring equalization of a received incoming signal subject tointersymbol interference (ISI), the apparatus comprising: a firstdecision feedback equalizer device which utilizes coefficients derivedfrom the estimated channel response and forms tentative symboldecisions; at least a second decision feedback equalizer device whichutilizes coefficients derived from the estimated channel response andthe tentative symbol decisions from the first decision feedbackequalizer to truncate the channel response to a desired channel memory;at least one non-linear equalizer device for providing equalization ofthe channel response over the desired memory, whereby the overallcomplexity of the equalizer is reduced by reducing the effective delayspread of the channel.

Still another aspect of the present invention provides for a method forreducing the complexity of an equalizer for use with a communicationsystem requiring equalization of a received incoming signal subject tointersymbol interference (ISI), the method comprising the steps of:deriving feedback and feed-forward coefficients for the associatedfeedback and feed-forward filters of a first and at least one subsequentdecision feedback equalizer from the estimated channel response;utilizing the first decision feedback equalizer to form tentativedecisions regarding certain symbols; utilizing at least one subsequentdecision feedback equalizer to truncate the channel response to adesired memory; utilizing at least one non-linear equalizer forproviding equalization of the channel response over the desired memory,whereby the overall complexity of the equalizer is reduced by reducingthe effective delay spread of the channel.

BRIEF DESCRIPTION OF THE DRAWINGS

Certain aspects and advantages of the present invention will be apparentupon reference to the accompanying description when taken in conjunctionwith the following drawings, which are exemplary, wherein:

FIG. 1 is a prior art representation of typical multipath channel with atime-decaying channel response.

FIG. 2 is a prior art diagram of an EDGE burst structure.

FIG. 3 is a prior art block diagram of representative transmitter,channel, and receiver.

FIG. 4 is a prior art block diagram of representative transmitterelements.

FIG. 5 is a prior art diagram of the encoding rule for an 8PSKmodulator.

FIG. 6 is a prior art diagram of the transmitted constellation for an8PSK signal corresponding to FIG. 5.

FIG. 7 is a block diagram of representative EDGE receiver elements,wherein the channel estimation might incorporate certain aspects of thepresent invention.

FIG. 8 is a prior art diagram of the auto-correlation of TrainingSequences.

FIG. 9 is a prior art block diagram of representative DFE elements, withan associated channel response after the feed-forward filter.

FIG. 10 is a block diagram, according to one aspect of the presentinvention, of certain representative elements of an equalizer whichcombines a DFE with a MAP equalizer.

FIG. 11 is a block diagram, according to one aspect of the presentinvention, of a representative channel response showing the resultingelements of the truncated channel.

FIG. 12 is a block diagram, according to one aspect of the presentinvention, of certain representative elements of the present equalizerwhich combines a DFE with a MAP equalizer, and then also employssubsequent DFE/MAP equalizers, as needed.

FIG. 13 is a flowchart, according to one aspect of the presentinvention, of certain representative steps that can be used to implementthe present method of equalization.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention is described below in terms of certain preferredembodiments, and representative applications. The apparatus andprocessing methods are applicable to any wireless or wirelinecommunication system where an equalizer is used to eliminate the ISIeffects of the channel.

A representative application of the invention is the EDGE system, and apreferred embodiment is described below. Since radio spectrum is alimited resource, shared by all users, a method must be devised todivide up the bandwidth among as many users as possible. The GSM/EDGEsystem uses a combination of Time- and Frequency-Division MultipleAccess (TDMA/FDMA). The FDMA part involves the division by the frequencyof the (maximum) 25 MHz bandwidth into 124 carrier frequencies spaced200 kHz apart. One or more carrier frequencies is assigned to each basestation. Each of these carrier frequencies is then divided in time,using a TDMA scheme. The fundamental unit of time in this TDMA scheme iscalled a burst period, and it lasts for 15/26 ms (or approximately 0.577ms). Eight burst periods are grouped into a TDMA frame (120/26 ms, orapproximately 4.615 ms) which forms the basic unit for the definition oflogical channels. One physical channel is one burst period per TDMAframe.

Many EDGE physical layer parameters are identical (or similar) to thoseof GSM. The carrier spacing is 200 kHz, and GSM's TDMA frame structureis unchanged. FIG. 2 shows a representative diagram 200 of an EDGE burststructure. One frame 202 is shown to include eight time slots. Eachrepresentative time slot 203 is shown to include a training sequence 204of 26 symbols in the middle, three tail symbols 206, 208 at either end,and 8.25 guard symbols 210 at one end. Each burst carries two sequencesof 58 data symbols. The data sequences 212 and 214 are shown on eitherside of the training sequence 204.

FIG. 3 next shows a prior art block diagram 300 of a communicationsystem that consists of a transmitter 304, a channel 310, and a receiver320. The signal s(t) 302 represents a sequence of information that isgoing to be transmitted over a channel. The transmitted signalencounters a channel 310 (which includes multiplicative, dispersivecomponent 312 and additive white Gaussian noise component 314). Thereceiver 320 attempts to recover the original signal s(t) as receivedinformation bits 322.

A more specific block diagram of the transmitter portion 400 is shown inFIG. 4. In particular this diagram is described in terms of GSM and EDGEapplications. The user data is first formatted into a frame via block402. Thereafter the data is convolutionally encoded and punctured asshown in block 404. The signal is passed to an interleaver 406 thatscrambles the coded bits and distributes them across four bursts, shownas the burst builder block 408. The GMSK or 8PSK modulator is shownreceiving the subsequent signal in block 410.

For 8PSK modulation, the modulating bits are mapped in groups of threeto a single 8PSK symbol. The encoding rule is shown in FIG. 5, where(d_(3i), d_(3i+1), d_(3i+2)) are the output bits from the interleaver.These output symbols are then continuously rotated by a phase shift of3π/8 radians per symbol (the symbol rate is approximately 270.833 ksps).These rotating 8PSK symbols are then pulse-shaped, using a filter withan impulse response corresponding to the main component in a Laurantdecomposition of a GMSK signal. As seen in FIG. 6, this partial responsesignaling (caused by the pulse-shaping filter) causes the transmittedsignal to have appreciable amounts of ISI.

The transmitted signal thereafter passes through a multipath fadingchannel h(t) and is corrupted by additive white Gaussian Noise n(t).Assuming that the span of the overall channel response is finite, thediscrete-time equivalent model of the received signal can be written as

$\begin{matrix}{{r_{n} = {{\sum\limits_{k = 0}^{L}{d_{n - k}h_{k}}} + \eta_{\eta}}},} & (1)\end{matrix}$where L is the span of the composite channel response (consisting of thecascade pulse-shaping filter, propagation channel and the receiverfront-end filter), dn is the nth transmitted data symbol, {h₀, h₁, . . ., h_(L)} are the complex coefficients of the channel response, and η_(η)is the complex, zero-mean, white Gaussian random variable.

A block diagram of a typical EDGE receiver 700 is shown in FIG. 7. Thereceived signal, after analog-to-digital conversion, is passed through adigital low-pass filter 702 (or matched filter) to enhance thesignal-to-noise ratio within the signal bandwidth of interest. Afeed-forward filter (FFF) 704 is used to try to convert the channel to aminimum-phase channel. The FFF coefficients are computed in block 708based on the channel estimates, which along with the sample timing arederived from the correlation of the received signal with a knowntraining sequence. The output from the FFF is passed to an equalizer706, which attempts to eliminate the ISI having the composite responsegiven by the transmitter pulse, the channel impulse response, and thereceiver filter. The equalizer might be a DFE, MLSE, or MAP. In block710, the output from the equalizer is then reassembled into a frame, anda deinterleaver is applied (if needed). This signal is then passed tothe channel decoder 712, if channel coding was applied at thetransmitter.

Timing recovery and channel estimation—the timing recovery and channelestimation are performed with the aid of the training sequence 204 (inFIG. 2). The training sequence has the property that the result ofcorrelating the middle 16 symbols with the entire training sequenceyields a correlation function with identically zero values for +/−5symbols around the peak 802, as shown in FIG. 8.

For timing recovery, the oversampled received signal is correlated withthe stored training sequence. The optimal symbol timing is given by theindex of the subsample with the largest correlation value. Once theoptimal symbol timing is determined, the estimates of the channelresponse, i.e., {h_(o), h₁, . . . , h_(L)} are given by a window of L+1symbol-spaced correlation values with the largest sum of energy. Sincethe auto-correlation values given by the training sequence areapproximately zero for up to +/−7 symbols around the peak 802, themaximum window size L may be as large as 7. Since the duration of theburst is 0.577 ms, the channel can be assumed to be stationary duringthe burst for most vehicle speeds of practical interest.

Certain well-known equalization techniques are next discussed, includingDFE and MLSE/MAP devices, followed by certain representative embodimentsof the proposed new technique.

Decision Feedback Equalizer—FIG. 9 shows a representative prior artblock diagram 900 of a DFE device, which might be used as the equalizerdevice above. A standard DFE consists of two filters, a feed-forwardfilter (FFF) 902 and a feedback filter (FBF) 904. The FFF is generallydesigned to act as a whitened matched filter to the received incomingsignal, thus maximizing the signal to noise ratio, while keeping thestatistical properties of the noise Gaussian with zero mean. Arepresentative signal (with interference) which might exist after theFFF is shown as 903, with signal rays h₀, h₁, h₂, and h₃. The FBF 904 isused to reconstruct post-cursor interference using decisions made onpreviously detected symbols. After filtering 904, the post-cursorinterference is subtracted from the output of FFF 902, and a symboldecision 908 is made on this output.

Accordingly, the input to the decision device, in discrete form, is asfollows:

$\begin{matrix}{{z_{n} = {{\sum\limits_{k = {- N_{f}}}^{0}{f_{k}r_{n - k}}} - {\sum\limits_{k = 1}^{N_{b}}{{\hat{d}}_{n - k}b_{k}}}}},} & (2)\end{matrix}$where f_(k), k=−N_(f), . . . , 0 are the coefficients of thefeed-forward filter, b_(k), k=1, . . . , N_(b) are the coefficients ofthe feedback filter, and {circumflex over (d)}_(n) denotes the decisionmade on the symbol d_(n). The number of the feedback coefficients N_(b)may be different from the memory of the overall channel response L.Hereafter, we will assume N_(b)=L. The coefficients of the FFF and theFBF for the DFE can be computed using a variety of computationallyefficient methods. One such method entitled “Fast Computation ofChannel-Estimate Based Equalizers in Packet Data Transmission” hasalready been incorporated by reference above.

Soft-decision decoding might also be applied to the outputs of the DFE.As shown in FIG. 7, the symbol decisions from the equalizer arede-interleaved and passed to the channel decoder. Since soft-decisiondecoding improves the performance, the hard symbol decisions output fromthe DFE are weighted with the appropriate channel gain before they arepassed to the decoder. Typically a hard-decision is made on the symbold_(n) which is then weighted by a soft-value s_(o), as given by thefollowing equation, to produce an appropriate weighting forsoft-decision decoding.

$\begin{matrix}{s_{o} = {\sum\limits_{k = 0}^{L}{h_{k}h_{k}^{*}}}} & (3)\end{matrix}$

Hence, the soft value is a function of the channel coefficients. Otherexamples include making the soft value proportional to the energy gainof the channel.

MLSE/MAP. An MLSE is the optimum equalizer in the presence of finite ISIand white Gaussian noise. The equalizer consists of a matched filterfollowed by a Viterbi algorithm. The complexity of the equalizer isdetermined by the number of states of the Viterbi algorithm, M^(L),where M is the symbol alphabet size and L is the memory of the channel.For high order modulations, such as 8PSK and 16QAM, the complexity ofthe equalizer is very large, even for moderate values of L.

Similar to the MLSE, the MAP criterion may be applied, resulting in anequalizer that has the same order of the complexity as the MLSE, but isable to produce soft symbol outputs. The soft symbol values improve theperformance of the subsequent channel decoder for a coded system.

For the MLSE or the MAP equalizer, the feed-forward filter can beimplemented as a matched filter with coefficients f_(−k)=h_(K)*, k=0, .. . , L. Although the noise samples after the matched filter arenon-white, the optimal path metric can be computed using the methoddescribed by Ungerboeck (see Gottfried Ungerboeck, “Adaptivemaximum-likelihood receiver for carrier-modulated data-transmissionsystem,” IEEE Transactions on Communications, vol. COM-22, No. 5, pp.624-636, May 1974). The path metric in the nth interval is given by:

$\begin{matrix}{{{Re}\left\lbrack {\alpha_{n}^{*}\left( {y_{n} - {\sum\limits_{i = l}^{L}{s_{i}\alpha_{n - i}}}} \right)} \right\rbrack},} & (4)\end{matrix}$where y_(n) is the output of the matched filter, α_(n) is thehypothetical input symbol and α_(n-i), i=1, . . . , L is given by thestate of the trellis, and s_(i) is given by the following convolution:

$\begin{matrix}{s_{i} = {\sum\limits_{k = 0}^{L - i}{h_{k}^{*}h_{k + i}}}} & (5)\end{matrix}$

For the MLSE, the hard symbol decisions output from the equalizer areweighed according to Equation (3) prior to being passed to the channeldecoder. The MLSE/MAP equalizers typically achieve better performanceover a DFE. Nevertheless, they are significantly more complex toimplement than the DFE for the same channel memory.

The proposed approach for equalizing 8PSK (or other such high-order)modulation signals consists of a combination of a DFE with a MAPequalizer (DFE-MAP). A block diagram of an embodiment of the presentinvention 1000 is shown in FIG. 10. The equalizer architecture consistsof two DFE-like structures 1002 and 1004, followed by a MAP equalizer1006. A feed-forward filter is shown as 1008. The first DFE 1002 actslike a conventional DFE and forms tentative symbol decisions. Thecoefficients of the feed-forward filter 1008 and the first feedbackfilter 1010 are derived from the channel estimates, as in theconventional DFE case. The coefficients of the second feedback filter1014 are a subset of the coefficients of the first feedback filter 1010.The input to the decision process 1012 is thus given by the priorEquation (2).

Accordingly, a sample channel response 1050 is shown after thefeed-forward filter 1008, containing signal rays h₀ through h₄. Thefirst DFE structure 1002 serves to first provide feedback signalsthrough the first feedback filter 1010 as shown by the signal rays h₁through h₄ in 1052.

The purpose of the second feedback filter 1014 is to eliminate theimpact of post-cursors (e.g., h₃ and h₄, shown by 1054) beyond L₁symbols (e.g., set at h₂), and thereby truncating the channel responseto a desired memory of L₁ symbols. The filter does this by cancelingthese post-cursors using the tentative decisions {circumflex over(d)}_(k) formed by the first DFE.

This is achieved by breaking the received signal after the feed-forwardfilter 1008 into two parts, as shown by Equation (4), and thereafterconstraining the maximum number of states in the MAP equalizer to beM^(L1) states out of a maximum possible of M^(L) for the full statespace.

$\begin{matrix}{{\sum\limits_{k = 0}^{L_{1}}{d_{n - k}b_{k}}} + {\sum\limits_{k = {L_{1} + 1}}^{L}{d_{n - k}b_{k}}} + \varphi_{n}} & (6)\end{matrix}$where φ is the noise sample at the symbol rate after passage through thewhitened-matched filter.

A tentative estimate of the data sequence,

{d̂_(n)}is produced by the first DFE structure 1002 (using hard symbolsdecisions of the z_(n) output of Equation (2)), and together with thefeedback coefficients, {b_(k)}, is used to limit the duration of theintersymbol interference to L₁ symbols.

Thus the input to the MAP equalizer becomes:

$\begin{matrix}{{{\sum\limits_{k = {- N_{f}}}^{0}{f_{k\;}r_{n - k}}} - {\sum\limits_{k = {L_{1} + 1}}^{L}{{\hat{d}}_{n - k}b_{k}}}},} & (7)\end{matrix}$where L₁<=L. Since the MAP equalizer now operates only on M^(L1) states,the overall complexity of the equalizer is significantly reduced.

For instance, with a channel memory of L=5, and a modulation order of 8(as used by 8PSK), a conventional MAP equalizer would require 8⁽⁵⁻¹⁾states, or 4096 states. By using the present system, the effectivechannel memory seen by the MAP would be reduced to 3 (see signal 1356)and the equalizer would only require 8⁽³⁻¹⁾ states, or 64 states. Withsubstantially fewer states, the proposed equalizer configuration wouldbe much more manageable and less complex to implement.

FIG. 11 next shows a graphical representation 1100 of thisrepresentative channel response having elements h₀ through h₄. When thevalue of L₁ (1102) is zero, the proposed equalizer degenerates to aconventional DFE, and when the value of the L₁=L (1104), the proposedequalizer is a full-state MAP equalizer. By choosing the appropriatevalue of L₁, certain performance and complexity trade-offs between a DFEand a full-state MAP equalizer can be made.

While not expressly shown, it should also be noted that an MLSEequalizer can be used instead of the MAP equalizer in the presentinvention. The MLSE device will further reduce the complexity of theimplementation but at the expense of receiver sensitivity. The presentinvention is not intended to be limited to the specific embodimentsshown above. FIG. 12 shows a block diagram having substantially the samecomponents (similarly numbered) as FIG. 10. After the MAP equalizer1006, however, a subsequent feedback filter 1204 is shown. The resultsof this subsequent feedback filter 1204 are then subtracted from theoutput of the feed-forward filter 1008. This signal is then fed into asubsequent MAP equalizer (represented at arrow 1208) to provide a result1212 which provides even better performance characteristics. Note thatthe arrows 1208 and 1210 are meant to indicate that even more feedbackfilters and MAP equalizers might be added, if further processing isneeded. Note that the addition of such subsequent filters will increasethe complexity of implementation, but (again) may provide for increasedperformance up to certain limits, wherein additional filters will not beworth their implementation cost.

FIG. 13 next shows a representative flowchart of certain steps 1300 thatmight be used to implement the present invention. In step 1302, anestimate is taken of the channel, which is shown receiving an incomingsignal 1301, as per the general approaches described above. In step1304, the feedback and feed-forward coefficients are derived for theassociated filters of the DFEs, based upon the estimate of the channelresponse. In step 1306, the signal passes through a feed-forward filterwhose coefficients have been determined above. In step 1308, a first DFE(including at least a feedback filter and decision process) is utilizedto form tentative symbol decisions. Step 1310 shows the second DFE beingused to cancel (or subtract) certain distant post-cursors. The number ofpost-cursors to be cancelled depends upon the memory of the channelresponse and the overall complexity desired (or a desired memory of thechannel) in the final implementation. The cancellation of suchpost-cursors serves to truncate the memory of the channel, whereby theoverall complexity of the equalizer is reduced by reducing the effectivedelay spread of the channel. Step 1312 next runs a MAP equalizer on thistruncated channel. Thereafter the resulting signal might be utilized(1314) as an equalized signal in any system that might require such anequalized signal.

Certain optional steps for implementation are shown in block 1315. Step1316 is shown canceling certain distant post-cursors (again, like 1310).This would be achieved by subsequent implementations of DFE components(i.e., feedback filters in association with feed-forward filters, andlinear equalizers) as implied by the arrows 1208 and 1210 in FIG. 12.Block 1318 next shows the step of utilizing a subsequent MAP equalizeron the constrained signal. Decision block 1320 inquires whether furtherprocessing is needed (or desired). If yes, then steps 1316 and 1318 canbe repeated as many times as might be needed with subsequent equalizerimplementations (again referring to elements 1208, 1210 in FIG. 12). Ifno further processing is needed, then the flow proceeds to step 1314where the resulting equalized signal is utilized.

Although the present invention has been particularly shown and describedabove with reference to specific embodiment(s), it is anticipated thatalterations and modifications thereof will no doubt become apparent tothose skilled in the art. It is therefore intended that the followingclaims be interpreted as covering all such alterations and modificationsas fall within the true spirit and scope of the invention.

The invention claimed is:
 1. An equalizer comprising: a decisionfeedback equalizer configured to receive an input signal, the decisionfeedback equalizer comprising a decision device and a first feedbackfilter coupled to the decision device in feedback fashion; a secondfeedback filter, separate from the first feedback filter, configured toreceive a decision from the decision device and to use the decision toproduce a cancellation signal; and a non-linear equalizer configured toreceive the cancellation signal and to produce an output signal based onthe cancellation signal.
 2. The equalizer of claim 1, wherein the secondfeedback filter is further configured to reduce the energy ofpost-cursor signal elements in the input signal that exist beyond apredetermined channel memory.
 3. The equalizer of claim 1, wherein thenon-linear equalizer comprises: a maximum likelihood sequence estimation(MLSE) equalizer.
 4. The equalizer of claim 1, wherein the non-linearequalizer comprises: a maximum a posteriori (MAP) equalizer.
 5. Theequalizer of claim 1, wherein the second feedback filter is furtherconfigured to cancel post-cursor signal elements in the input signalthat exist beyond a predetermined channel memory.
 6. The equalizer ofclaim 1 further comprising: a feedforward filter configured to receivean incoming signal and to increase a signal-to-noise ratio of theincoming signal to provide the input signal.
 7. A method of processing acommunication signal, comprising: processing, by a decision feedbackequalizer, an input signal to produce a decision signal, the decisionfeedback equalizer including: a decision device; and a first feedbackfilter coupled to the decision device in feedback fashion; processing,by a second feedback filter, the decision signal to produce acancellation signal, wherein the second feedback filter is separate fromthe first feedback filter; and generating, by a nonlinear equalizer, anoutput signal based on the cancellation signal.
 8. The method of claim7, wherein the processing by the second feedback filter furthercomprises: reducing the energy of post-cursor signal elements in theinput signal that exist beyond a predetermined channel memory.
 9. Themethod of claim 7, wherein the generating comprises: generating theoutput signal using a maximum likelihood sequence estimation (MLSE)non-linear equalizer.
 10. The method of claim 7, wherein the generatingcomprises: generating the output signal using a maximum a posteriori(MAP) equalizer.
 11. The method of claim 7, wherein the processing bythe second feedback filler further comprises: cancelling post-cursorsignal elements in the input signal that exist beyond a predeterminedchannel memory.
 12. The method of claim 7, further comprising:processing an incoming signal using a feedforward filter to increase asignal-to-noise ratio of the incoming signal to provide the inputsignal.
 13. An equalizer, comprising: a feed forward filter configuredto filter a signal according to a plurality of filter coefficients toprovide an input signal, the plurality of filter coefficients beingbased on a channel estimate of the signal; a first decision feedbackequalizer configured to provide a decision signal, wherein the decisionsignal is based on a difference between the input signal and a filteredsignal, and wherein the filtered signal is provided by filtering thedecision signal according to the plurality of filter coefficients; asecond decision feedback equalizer configured to provide a cancellationsignal by filtering the decision signal according to a subset of theplurality of filter coefficients; and a non-linear equalizer configuredto provide an output signal based on a difference between the inputsignal and the cancellation signal.
 14. The equalizer of claim 13,further comprising: a feedback filter configured to filter the outputsignal to provide a second cancellation signal; and a second non-linearequalizer configured to produce a second output signal based on thesecond cancellation signal.
 15. The equalizer of claim 13, wherein thenon-linear equalizer comprises: a maximum likelihood sequence estimation(MLSE) non-linear equalizer; or a maximum a posteriori (MAP) equalizer.16. The equalizer of claim 1, further comprising: a third feedbackfilter configured to filter the output signal to provide a secondcancellation signal; and a second non-linear equalizer configured toproduce a second output signal based on the second cancellation signal.17. The equalizer of claim 1, wherein the decision device is furtherconfigured to provide the decision as part of a decision signal, whereinthe first feedback filter is further configured to filter the decisionsignal according to a plurality of filter coefficients; and wherein thesecond feedback filter is farther configured to produce the cancellationsignal by filtering the decision signal according to a subset of theplurality of filter coefficients.
 18. The equalizer of claim 1, whereinthe non-linear equalizer is further configured to process a filteredsignal according to a state space, the filtered signal beingrepresentative of a difference between the cancellation signal and theinput signal to provide the output signal, and wherein the state spaceis less than a full state space corresponding to M^(L), M beingrepresentative of a size of a symbol alphabet used for modulation of theinput signal, and L being representative of a channel memorycorresponding to the input signal.
 19. The method according to claim 7,further comprising: processing, by a third feedback filter, the outputsignal to produce a second cancellation signal; and generating, by asecond non-linear equalizer, a second output signal based on the secondcancellation signal.
 20. The method according to claim 7, wherein theprocessing by the decision feedback equalizer comprises: filtering thedecision signal according to a plurality of filter coefficients toprovide a filtered signal; and subtracting the filtered signal from theinput signal to provide an input to the decision device, and wherein theprocessing by the second feedback filter comprises: filtering thedecision signal according to a subset of the plurality of filtercoefficients to provide the cancellation signal.